Atomistic Simulations of Effect of Coulombic Interactions on Carrier Fluctuations in Doped Silicon
- PDF / 368,315 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 14 Downloads / 199 Views
D5.7.1
Atomistic Simulations of Effect of Coulombic Interactions on Carrier Fluctuations in Doped Silicon Zudian Qin and Scott T. Dunham University of Washington, Department of Electrical Engineering, Seattle WA 98195, U.S.A.
ABSTRACT Carrier distributions associated with point charges in silicon solved with quantum perturbation theory are used to determine Coulombic interactions between charged defects in the presence of carrier screening. The resulting interactions are used in kinetic lattice Monte Carlo (KLMC) simulations of point defect-mediated diffusion to study dopant redistribution and associated variations in carrier concentration. Over a broad range of doping concentrations and temperatures, Coulombic repulsion between like dopants leads to ordering, resulting in a more uniform electrical potential distribution and therefore reduced variations in device performance compared with random doping, the standard condition assumed in previous doping fluctuation analyses.
INTRODUCTION Fluctuations in carrier density due to both dopant number and location variations have been identified as a critical issue in controlling device performance (e.g., threshold voltage Vth variations control) in nanoscale MOSFETs [1-3]. To date, analysis of this phenomenon has largely assumed that the dopants are distributed randomly within active regions [4-8]. However, interactions between dopants during device fabrication can lead to correlations in dopant locations, modifying the resulting variations. One source of such correlations is the Coulombic interactions between ionized dopants, screened by nearby free carriers. In this work, we examine the effect of these interactions on variations in electrical potential within doped regions via kinetic lattice Monte Carlo (KLMC) simulations [9-11], which simultaneously solve for free carrier distributions and include the effect of associated potential variations on the diffusion of charged dopants and point defects. To study doping fluctuations, a tool must first be capable of tracking dopant locations within the system. Traditional continuum simulators lack such capability since they focus on macroscopic-level averages (e.g., dopant concentrations) within the system without giving any information on locations of individual atoms. Kinetic lattice Monte Carlo simulations, on the other hand, are well suited to this task. The KLMC simulations utilized in this work operate on a 3D silicon (diamond) lattice structure with impurities and point defects mapped to lattice sites [911]. The system evolves through transitions from one atomic configuration to the next, by virtue of point defect migration/reactions. The rates of these transitions are determined by the migration barriers combined with changes in system energy associated with transitions: E − Ef − Em exp i k BT 2k B T
ν = ν 0 exp
(1)
D5.7.2
where Em is the unbiased migration barrier, Ei and Ef are the system energies before and after the transition, and T is the system temperature. The system energies a
Data Loading...
